1. by Dr. Jaafar A. MohammedJaafar.brifkani@uod.ac University of Duhok (UOD) College of Engineering 9/17/2023 1

2. Dr. Jaafar A. Brifkani Lecturer University of Duhok Jaafar.brifkani@.uod.ac Presenter Biography Dr. Brifkani is a Lecturer in the Department of Civil Engineering at the University of Duhok, specializing in Geotechnical Engineering (Tunnels Structure). His activity: Research published in international conferences and journals : 20 Number of Textbook: 7 Languages: Kurdish, Arabic, English and Czech You can find him at this links by writing his name as Jaafar Mohammed or Ing. Jaafar Mohammed. https://uod.ac/ac/c/coe/departments/ce/members/jaafar-abdullah-mohammed/ https://www.linkedin.com/in/dr-jaafar-abdullah-mohammed-1857373a/ https://orcid.org/0000-0001-9999-2414 https://publons.com/researcher/2268936/dr-jaafar-a-mohammed/ http://web.uod.ac/ac/c/coe/centers/research-center/ https://scholar.google.com/citations?user=24oVLqsAAAAJ&hl=en https://www.researchgate.net/profile/Jaafar_Mohammed3 https://oud.academia.edu/DrJaafarMohammed https://slideplayer.com/slide/13259594/ Academic Qualifications  PhD Degree in Civil Engineering, College of Engineering, VŠB - Technical University of Ostrava, Ostrava-Poruba, Czech Republic, class 2020  Master Degree in Civil Engineering, College of Engineering, VŠB - Technical University of Ostrava, Ostrava-Poruba, Czech Republic, class 2009  B.Sc. in Civil Engineering, College of Engineering, VŠB - Technical University of Ostrava, Ostrava- Poruba, Czech Republic, class 2007  B.Sc.in in Civil Engineering, College of Engineering, Duhok University, Kurdistan Region Iraq class, 2000. 9/17/2023 2 Dr. Jaafar A. Brifkani

3. Student's Obligation Class attendance and/or online learning Commitment Assessment 1.Quizzes 10 % 2.Homework 5 % 3.Assignments 5 % 4.Mid-Term exam. 20 % 5.Final Exam. 60 % 9/17/2023 3 Dr. Jaafar A. Brifkani

4. Objectives 1.Learn the basic scientific concepts of theoretical and analytical skills relevant to the stresses and strain; shearing force and bending; as well as torsion and deflection of different structural elements. 2.Know how to compute normal and shearing strains and stresses in mechanically loaded members (axial loading). 3.Understand the difference between statically determinate and indeterminate problems. 4.Understand and carry out simple experiments illustrating properties of materials in tension, compression as well as hardness and impact tests. 5.Analyze stresses and understand the concepts of principal stresses and the use of Mohr circles to solve two-dimensional stress problems. 6.Draw shear force and bending moment diagrams of simple beams and understand the relationships between loading intensity, shearing force and bending moment. 9/17/2023 4 Dr. Jaafar A. Brifkani

5. References‌ 1.Ferdinand P. Beer, E. Russell Johnston, John T. Dewolf and David F. Mazurek, 2012. MECHANICS OF MATERIALS, SIXTH EDITION. ISBN 978-0-07- 338028-5. 2.William A. Nash and Merle C. Potter, 2011. Strength Of Materials - Fifth Edition. ISBN: 978-0-07-163507-3. 3.Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, David F. Mazurek (2015). Mechanics of Materials. McGraw-Hill, 7th Edition. 4.Barry J. Goodno and James M. Gere, 2018. Mechanics of Materials, Ninth Edition. Library of Congress Control Number: 2016952400 ISBN: 978-1-337- 09334-7. 5.Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, David F. Mazurek (2012). Mechanics of Materials. McGraw-Hill, 6th Edition. 6.Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, David F. Mazurek (2006). Mechanics of Materials. McGraw-Hill, 4th Edition. 7.Hibbeler R.C. (2010). Mechanics of Materials. Pearson Education Inc. Singapore, 8th Edition in SI Units. 8.R. C. HIBBELER, 2014. MECHANICS OF MATERIALS, NINTH EDITION. ISBN 13: 978-0-13-325442-6 9/17/2023 5 Dr. Jaafar A. Brifkani

6. Greek Alphabet 9/17/2023 6 Dr. Jaafar A. Brifkani

7. Introduction The important mechanical properties of materials are: elasticity, plasticity, strength, ductility, hardness, brittleness, toughness, stiffness, resilience/ flexibility, creep, etc. In determining the fabrication works and possible practical applications, the mechanical properties of materials, their strength, rigidity and ductility are of vital importance. There are several materials behave quite differently when stressed in different ways, e.g. steel and wood are stronger in tension whereas cast iron, cement and bricks are much stronger in compression. Obviously, stresses can produce a shape change and may also cause a material to break or fracture. The combination of high yield strength and good fracture toughness or ductility makes steel an excellent structural material. Bodies can be classified as rigid bodies, resistant bodies and deformable bodies. 9/17/2023 7 Dr. Jaafar A. Brifkani

8. Introduction The difference(s) between Engineering Mechanics & Strength of Materials The basic and main difference is in Mechanics we assume the bodies to be rigid but in strength of materials bodies are considered to be deformed under elastic limit or condition. Definition. In the mechanics of materials, the strength of a material is its ability to withstand an applied load without failure or plastic deformation. The field of strength of materials deals with forces and deformations that result from their acting on a material. Strength of materials introduces many important topics include normal stress and strain, axial deformation, statically indeterminant problems, torsion, shear and moment diagrams, bending stress, shear stress, beam deflection, and stress transformations, amongst others. 9/17/2023 8 Dr. Jaafar A. Brifkani

9. Introduction The difference(s) between Engineering Mechanics & Strength of Materials. https://sme.hust.edu.vn/en/ department- center/material-mechanic- structure 9/17/2023 9 Dr. Jaafar A. Brifkani

10. Why we need to know about materials? Materials science teaches us what things are made of and why they behave as they do. Stuff is made of stuff 1.what should your part be made of? 2.what does it have to do? 3.how thick should you make it The properties we usually care about are: 1.stiffness / hardness 2.thermal conductivity 3.heat capacity 4.coefficient of thermal expansion 5.density 6.damage potential 7.machine-ability 8.surface condition, etc. 9/17/2023 10 Source: UCSD: Physics 121; 2012 Dr. Jaafar A. Brifkani

11. Mechanical Properties Isotropy vs Anisotropy: The Greek prefix “an” denotes a difference in meaning and application from the base or root word. The underlying word in this case is “isotropic,” which means “equal direction.” “Iso” is a Greek word that means “equal,” while “tropic” means “direction” in Greek. Isotropic minerals have the same physical and chemical properties in all directions, while anisotropic minerals have different properties in different directions. Difference between Isotropic and Anisotropic 9/17/2023 11 Dr. Jaafar A. Brifkani

12. Mechanical Properties 9/17/2023 12 Elasticity: It is the property of a material which enables it to regain its original shape and size after deformation within the elastic limit. However, in nature no material is perfectly elastic, i.e., a certain limit exists for every material beyond which it will not be able to regain its original shape and size. This limit is termed as elastic limit. Dr. Jaafar A. Brifkani Plasticity: It is the ability of material to be permanently deformed (without fracture) even after the load is removed. It is of importance in deciding manufacturing processes like forming, shaping, extruding operations etc. Metals possess more plasticity at high temperatures. Usually, plasticity of a material increases with increase in temperature.

13. Mechanical Properties: cont. 9/17/2023 13 Ductility: It is defined as the property of a metal by virtue of which it can be drawn into wires or elongated before rupture takes place. It is measured by the percentage of elongation and the percentage of reduction in area before rupture of test piece. Dr. Jaafar A. Brifkani Strength: It may be defined as the capacity of material by virtue of which it can withstands or support an external force or load with rupture. It is expressed as force per unit area of cross-section. This is most important property of a metal, which plays a decisive role in designing various structures and components.

14. Ultimate strength: It is the load required to fracture a unit cross-section of material. Types of strengths Elastic Strength: It is the value of strength corresponding to transition from elastic to plastic range, i.e. when material changes its behavior from elastic range to plastic range. 9/17/2023 14 Dr. Jaafar A. Brifkani Stress-Strain Curve

15. Plastic strength: It is the value of strength of the material which corresponds to plastic range and rupture. It is also termed as ultimate strength. In actual practice, a specimen is subjected to a stress which is always less than the working stress. The ratio of ultimate stress to the working stress of a metal is termed as factor of safety or factor of ignorance. This greatly depends upon the nature of loads or stresses. Types of strengths: cont. 9/17/2023 15 Dr. Jaafar A. Brifkani

16. Concept of Force Force The interaction between two bodies (materials) is generate a force. Forces may be applied through actual contact of the bodies or at a distance (e.g., gravity). When a force acts on a body tending to produce deformation, a resistance is developed to this external force application. by Wayne Anderson 9/17/2023 16 Example of the internal forces in an idealized console-bar structure Dr. Jaafar A. Brifkani

17. There are several types of forces A Force is any push or pull on an object. Balanced Forces occur when two or more forces act in different directions on an object and the net force is zero. Unbalanced Force occur when two or more forces act in different directions on an object and a net force occurs in the direction of the larger force. 9/17/2023 17 Dr. Jaafar A. Brifkani

18. There are several types of forces: cont. Normal force: The contact force, when an object pushes on a surface, the surface pushes back on the object perpendicular to the surface. Friction force: This force occurs when a surface resists sliding of an object and is parallel to the surface. Tension force: A pulling force exerted on an object by a rope or cord. Weight/ Gravitational Force: The long-range force, pull of gravity on an object. by Wayne Anderson 9/17/2023 18 Dr. Jaafar A. Brifkani

19. Simulating a force into its component vectors Choose perpendicular x and y axes. F x and F y are the components of a force along these axes. Use trigonometry to find these force components. by Wayne Anderson 9/17/2023 19 If stresses are known, we can also define the internal forces as three force components and three moment components in terms of stresses. Dr. Jaafar A. Brifkani

20. Newton’s Law Newton’s First Law (law of inertia) Newton’s first law of motion states that an object at rest will remain at rest, and an object moving at a constant velocity will continue moving at a constant velocity, unless it is acted upon by an unbalanced force. 9/17/2023 20 Newton’s Second Law Force = Mass x Acceleration, (F = ma) Force is measured in Newton's Acceleration of Gravity(Earth) = 9.8 m/s ² Weight (force) = mass x gravity (Earth) Dr. Jaafar A. Brifkani

21. Newton’s Law Newton’s Third Law If you exert a force on a body, the body always exerts a force (the “reaction”) back upon you. A force and its reaction force have the same magnitude but opposite directions. These forces act on different bodies. by Wayne Anderson 9/17/2023 21 Hooke’s Law Hooke’s Law: In 1678, Robert Hooke, for the first time stated that within elastic limits, stress is proportional to strain, i.e. F= - kx F = restoring force of spring x = the distance that the spring has been stretch or compressed from equilibrium k = the spring constant (-) = force acts in opposite direction of the displacement Dr. Jaafar A. Brifkani

22. Hooke’s Law For any material having a stress-strain curve of the form shown in figure, it is evident that the relation between stress and strain is linear for comparatively small values of the strain. This linear relation between elongation and the axial force causing it is called Hooke’s law. 9/17/2023 22 To describe this initial linear range of action of the material we may consequently write ( σ = Eε ). where E denotes the slope of the straight-line portion OP of each of the curves in Figs.(a), (b), and (c). The quantity E, i.e., the ratio of the unit stress to the unit strain, is the modulus of elasticity of the material in tension, or, as it is often called, Young’s modulus” E” has the same units as does the stress, N/m 2 Dr. Jaafar A. Brifkani

23. Axially Loaded Bar Rigid Body A rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it. A rigid body can be considered as a combination of a large number of particles in which all the particles remain at a fixed distance from one another, both before and after applying a load. 9/17/2023 23 Dr. Jaafar A. Brifkani Railroad wheel –rigid body

24. Axially Loaded Bar 9/17/2023 24 Dr. Jaafar A. Brifkani

25. Axially Loaded Bar Deformable body A deformable body is a physical body that deforms, meaning it changes its shape or volume while being acted upon by an external force. 9/17/2023 25 The simplest case to consider at the start is that of an initially straight metal bar of constant cross section, loaded at its ends by a pair of oppositely directed collinear forces coinciding with the longitudinal axis of the bar and acting through the centroid of each cross section. For static equilibrium the magnitudes of the forces must be equal. If the forces are directed away from the bar, the bar is said to be in tension; if they are directed toward the bar, a state of compression exists. Dr. Jaafar A. Brifkani

26. Break We will continue in the next lecture